lsm3241: bioinformatics and biocomputing lecture 6: fundamentals of molecular modeling prof. chen yu...

LSM3241: Bioinformatics and LSM3241: Bioinformatics and BiocomputingBiocomputing

Lecture 6: Fundamentals of Molecular ModelingLecture 6: Fundamentals of Molecular Modeling

Prof. Chen Yu ZongProf. Chen Yu Zong

Tel: 6516-6877Tel: 6516-6877Email: Email: csccyz@nus.edu.sgcsccyz@nus.edu.sg

http://http://bidd.nus.edu.sgbidd.nus.edu.sgRoom 07-24, level 7, SOC1, Room 07-24, level 7, SOC1,

National University of SingaporeNational University of Singapore

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Structural organization of a moleculeStructural organization of a molecule

Three features:

• Configuration (atom organization).

• Conformation (atom spatial arrangement).

• Shape (Surface landscape, steric packing)

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Structural organization of a moleculeStructural organization of a moleculeI. Configuration:  

• The organization of atoms and chemical bonds.   • Change of configuration requires breaking of bonds.

Switch between H and NH2 requires bond breaking.

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Structural organization of a moleculeStructural organization of a molecule

An important aspect of configuration is chirality

• Chirality defines the property of mirror image.

The image on the right is an mirror image of the one at left.

• If mirror image is not the same as the original, the compound is called chiral.

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Structural organization of a moleculeStructural organization of a molecule

Example of chiral and non-chiral compound:

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Structural organization of a moleculeStructural organization of a molecule

II. Conformation:  

• Determined by the spatial positions of its constituent atoms.

  • Inter-convertible without breaking and making bonds

Rotatable bond

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Protein structure and conformation change:Protein structure and conformation change:

Movie Show:

Drug Binding Induced Conformation Change in Protein

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Structural organization of a moleculeStructural organization of a molecule

III. Shape  

• Steric packing (what part of space is covered by the compound).  

• Surface features (cavities, grooves where other molecules can bind to).

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Protein Surface Determines Its Interaction with Protein Surface Determines Its Interaction with Other Molecules:Other Molecules:

Protein-Protein InteractionProtein-Protein Interaction

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Protein Surface Determines Its Interaction with Protein Surface Determines Its Interaction with Other Molecules:Other Molecules:

Protein-DNA InteractionProtein-DNA Interaction

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Protein Surface Determines Its Interaction with Protein Surface Determines Its Interaction with Other Molecules:Other Molecules:

Protein-RNA InteractionProtein-RNA Interaction

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Protein Surface Determines Its Interaction with Protein Surface Determines Its Interaction with Other Molecules:Other Molecules:

Protein-Drug InteractionProtein-Drug Interaction Mechanism of Drug Action:

A drug interferes with the function of a disease protein by binding to it.

This interference stops the disease process

Drug Design:

Structure of disease protein is very useful

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Atomic motions in a molecule Atomic motions in a molecule

• Atoms are not rigidly positioned.

• External and internal forces can induce atomic motions.

• Some motions have chemical effect. Movie Show:

Protein transient opening for ligand or drug binding and dissociation:

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Atomic motions in a molecule Atomic motions in a molecule

The effect of motions are described by energy:    

Energy measures the ability to do work.

  Motion is associated

with energy.

Movie Show:

Protein transient opening for ligand or drug binding and dissociation:

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Types of EnergyTypes of Energy Kinetic energy -- motional energy

Kinetic energy is related to the speed and mass of a moving object. The higher the speed and the heavier the object is, the bigger work it can do.  

Potential Energy -- "positional" energy.  Water falls from higher ground to lower ground. In physics such a phenomenon is

modeled by potential energy description:

Objects move from higher potential energy place to lower potential energy place.

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Potential Energy Description of Molecular MotionsPotential Energy Description of Molecular Motions  A molecule changes from higher potential energy form to lower potential energy

form.

Potential energy is determined by inter-molecular, intra-molecular, and environmental forces

The total energy of motions is: Energy = Stretching Energy + Angle Bending Energy +Torsion Energy + Non-Bonded Interaction Energy

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

The stretching energy equation is based on Hooke's law. The "kb" parameter controls the stiffness of the bond spring, while "ro" defines its equilibrium length.

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

The stretching energy equation is based on Hooke's law. The "kb" parameter controls the stiffness of the bond spring, while "ro" defines its equilibrium length.

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

The bending energy equation is also based on Hooke's law

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

The bending energy equation is also based on Hooke's law

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

The torsion energy is modeled by a simple periodic function

Why?

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

Torsion energy as a function of bond rotation angle.

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

The non-bonded energy accounts for repulsion, van der Waals attraction, and electrostatic interactions.

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

• van der Waals attraction occurs at short range, and rapidly dies off as the interacting atoms move apart.

• Repulsion occurs when the distance between interacting atoms becomes even slightly less than the sum of their contact distance.

• Electrostatic energy dies out slowly and it can affect atoms quite far apart.

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

Types of Hydrogen Bond:

N-H … ON-H … NO-H … NO-H … O

Can be modeled by

• VdW+electrostatic (AMBER)• Modified Linard-Jones (CHARM)• Morse potential (Prohofsky/Chen)

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

Complete Energy Function:

bondednon ijij

ji

ij

ij

ij

ijrra

bondH

bondS

rra

rotationbond

n

eqbendinganglebond

eqrstretchbondatoms

r

qq

r

B

r

AVeV

VeVn

v

krrkm

pH

][])1([

])1([)]cos(1[

2

)(2

1)(

2

1

2

61202)(

0

02)(

0

222

'0

'0

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

Concept of energyscale is Important for molecular Modeling

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

Concept of energy scale is Important for molecular modeling

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Molecular Modeling: Molecular Modeling: Basic Interactions and Their ModelsBasic Interactions and Their Models

Sources of force parameters:

Bonds, VdW, Electrostatic (for amino acids, nucleotides only):• AMBER: J. Am. Chem. Soc. 117, 5179-5197• CHARMM: J. Comp. Chem. 4, 187-217

H-bonds (Morse potential):• Nucleic Acids Res. 20, 415-419.• Biophys. J. 66, 820-826

Electrostatic parameters of organic molecules need to be computed individually by using special software (such as Gaussian)

bondednon ijij

ji

ij

ij

ij

ijrra

bondH

bondS

rra

rotationbond

n

eqbendinganglebond

eqrstretchbondatoms

r

qq

r

B

r

AVeV

VeVn

v

krrkm

pH

][])1([

])1([)]cos(1[

2

)(2

1)(

2

1

2

61202)(

0

02)(

0

222

'0

'0

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Molecular Modeling: Molecular Modeling:

bondednon ijij

ji

ij

ij

ij

ijrra

bondH

bondS

rra

rotationbond

n

eqbendinganglebond

eqrstretchbondatoms

r

qq

r

B

r

AVeV

VeVn

v

krrkm

pH

][])1([

])1([)]cos(1[

2

)(2

1)(

2

1

2

61202)(

0

02)(

0

222

'0

'0

Modeling Method I: Conformation search:

Change each torsion angle: Phi -> Phi+dphiSubsequent change of atom positions: xi -> xi+dxi; yi -> yi+dyi; zi -> zi+dziEnergy is changed: E -> E +dE

Each set of torsion angles corresponds to a conformation.Find sets with lower energy

All possible states can be explored

3131

Molecular Modeling: Molecular Modeling:

bondednon ijij

ji

ij

ij

ij

ijrra

bondH

bondS

rra

rotationbond

n

eqbendinganglebond

eqrstretchbondatoms

r

qq

r

B

r

AVeV

VeVn

v

krrkm

pH

][])1([

])1([)]cos(1[

2

)(2

1)(

2

1

2

61202)(

0

02)(

0

222

'0

'0

Modeling Method II: Energy minimization:

Force guided approach:

Initialize: Change atom position: xi -> xi+dxi

Compute potential energy change: V -> V +dV

Determine next movement:

Force: Fxi=-dV/dxi; Fyi=-dV/dyi; Fzi=-dV/dziAtom displacement: dxi=C*FxiNew position: xi=xi+dxi

Energy minimization can only go down hill. Why?

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Summary of Today’s lectureSummary of Today’s lecture

• Structural organization of a molecule.• Basic interactions and models• Modeling methods (conformation search, energy

minimization)